Question
Solve the equation. (Enter your answers as a comma-separated list.) \( x=\square \) \( x^{3 / 2}=64 \)
Ask by Fernandez Donnelly. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 16 \)
Solution
1. We start with the equation:
\[
x^{\frac{3}{2}} = 64
\]
2. Rewrite \( x^{\frac{3}{2}} \) as \((\sqrt{x})^3\):
\[
(\sqrt{x})^3 = 64
\]
3. Take the cube root of both sides:
\[
\sqrt{x} = \sqrt[3]{64}
\]
Since \(\sqrt[3]{64} = 4\), we have:
\[
\sqrt{x} = 4
\]
4. Square both sides to solve for \(x\):
\[
\left(\sqrt{x}\right)^2 = 4^2
\]
\[
x = 16
\]
The solution is: \(16\)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To solve the equation \( x^{3/2} = 64 \), first, we can rewrite it as \( x^{3/2} = 64 \). To isolate \( x \), we will raise both sides to the power of \( \frac{2}{3} \): \[ x = (64)^{\frac{2}{3}} \] Calculating \( 64^{\frac{1}{3}} \) gives us 4 (since \( 4 \times 4 \times 4 = 64 \)). Now, squaring this result: \[ x = 4^2 = 16 \] So, the solution is \( x = 16 \). Final answer: \( x = 16 \)
